Ninth Biennial Meeting of the Cognitive Development Society
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Origins of Numerical Knowledge
Mathematical Cognition, 1995, Vol. 1, pp. 35-60. Origins of Numerical Knowledge Karen Wynn University of Arizona I would like to thank Renee Baillargeon, Tom Bever, Paul Bloom, Randy Gallistel, Rochel Gelman, Marcus Giaquinto and Elizabeth Spelke for helpful discussion, and Marcus Giaquinto and especially Paul Bloom for their painstaking comments on preliminary versions of this paper. Some of the work presented here was supported by an NICHD FIRST Award to the author. Correspondence and comments should be sent to the author at the Department of Psychology, University of Arizona, Tucson AZ 85721; or sent by e-mail to [email protected]. Wynn, K. Origins of Numerical Knowledge Abstract Evidence is presented that young human infants possess a system of numerical knowledge that consists of a mechanism for determining and representing small numbers of entities, as well as procedures for operating over these representations so as to extract information of the numerical relationships between them. A model for this mechanism is presented, and its relation to the development of further numerical knowledge is discussed. - 2 - Wynn, K. Origins of Numerical Knowledge Introduction In this paper, I will make three central arguments. First, I will argue that human infants possess extensive numerical competence. Empirical findings show that young infants are able to represent and reason about numbers of things. Infants' ability to determine number is not based on perceptual properties of displays of different numbers of items, nor is it restricted to specific kinds of entities such as physical objects. Rather, it spans a range of ontologically different kinds of entities. -
Page 2 All the World's a Stage, and All the Men and Women Merely
Page 2 All the world's a stage, And all the men and women merely players. They have their exits and their entrances; and one man in his time plays many parts. —WILLIAM SHAKESPEARE English Playwright, 17th Century The Life-Span Perspective Page 3 This book is about human development—its universal features, its individual variations, its nature. Every life is distinct, a new biography in the world. Examining the shape of life-span development allows us to understand it better. Life-Span Development is about the rhythm and meaning of people's lives, about turning mystery into understanding, and about weaving a portrait of who each of us was, is, and will be. In Section 1, you will read “Introduction” (Chapter 1). Page 4 chapter outline 1 The Life-Span Perspective Learning Goal 1 Discuss the distinctive features of a life-span perspective on development. The Importance of Studying Life-Span Development Characteristics of the Life-Span Perspective Some Contemporary Concerns 2 The Nature of Development Learning Goal 2 Identify the most important processes, periods, and issues in development. Biological, Cognitive, and Socioemotional Processes Periods of Development The Significance of Age Developmental Issues 3 Theories of Development Learning Goal 3 Describe the main theories of human development. Psychoanalytic Theories Cognitive Theories Behavioral and Social Cognitive Theories Ethological Theory Ecological Theory An Eclectic Theoretical Orientation 4 Research in Life-Span Development Learning Goal 4 Explain how research on life-span development is conducted. Methods for Collecting Data Research Designs Time Span of Research Conducting Ethical Research Minimizing Bias Page 5 T ed Kaczynski sprinted through high school, not bothering with his junior year and making only passing efforts at social contact. -
Perception of Partly Occluded Objects in Infancy
COGNITIVE PSYCHOLOGY 15, 483-524 (1983) Perception of Partly Occluded Objects in Infancy PHILIP J. KELLMAN AND ELIZABETH S. SPELKE University of Pennsylvania Four-month-old infants sometimes can perceive the unity of a partly hidden object. In each of a series of experiments, infants were habituated to one object whose top and bottom were visible but whose center was occluded by a nearer object. They were then tested with a fully visible continuous object and with two fully visible object pieces with a gap where the occluder had been. Patterns of dishabituation suggested that infants perceive the boundaries of a partly hidden object by analyzing the movements of its surfaces: infants perceived a connected object when its ends moved in a common translation behind the occluder. Infants do not appear to perceive a connected object by analyzing the colors and forms of surfaces: they did not perceive a connected object when its visible parts were stationary, its color was homogeneous, its edges were aligned, and its shape was simple and regular. These findings do not support the thesis, from gestalt psy- chology, that object perception first arises as a consequence of a tendency to perceive the simplest, most regular configuration, or the Piagetian thesis that object perception depends on the prior coordination of action. Perception of ob- jects may depend on an inherent conception of what an object is. The objects that surround a perceiver, at any point of observation, are only partly in view. Every object’s back is occluded by its front, and even its front may be partly concealed by other things. -
Baillargeon, R. (1999)
PERSPECTIVES ON PSYCHOLOGICAL SCIENCE Innate Ideas Revisited For a Principle of Persistence in Infants’ Physical Reasoning Rene´e Baillargeon University of Illinois at Urbana-Champaign ABSTRACT—The notion of innate ideas has long been the example, the behaviorism of John B. Watson (1924) and B.F. subject of intense debate in the fields of philosophy and Skinner (1938) or the constructivism of Jean Piaget (1954). cognitive science. Over the past few decades, method- The notion of innate ideas was finally revived in the mid-20th ological advances have made it possible for developmental century when the linguist Noam Chomsky (1965) proposed that researchers to begin to examine what innate ideas—what human infants are born with a universal grammar that makes innate concepts and principles—might contribute to in- possible their rapid acquisition of language. Chomsky’s theory fants’ knowledge acquisition in various core domains. This departs from earlier rationalist proposals in at least two article focuses on the domain of physical reasoning and on significant ways. First, the universal grammar is understood to Spelke’s (1988, 1994) proposal that principles of continuity be an unconscious language-acquisition system, rather than a and cohesion guide infants’ interpretation of physical set of ideas that can be brought to consciousness by appropriate events. The article reviews recent evidence that these two triggers. Second, the system is construed as a biological adap- principles are in fact corollaries of a single and more tation whose existence is rooted in the process of evolution, powerful principle of persistence, which states that objects rather than in metaphysics (for reviews, see Chomsky, 1965; persist, as they are, in time and space.